Calculating the distance between polygon and point in R

Question

I have a, not necessarily convex, polygon without intersections and a point outside this polygon. I\'m wondering how calculate the Euclidian distance most efficiently in a 2

Answer 1

I used distm() function in geosphere package to calculate the distence when points and apexes are presented in coordinate system. Also, you can easily make some alternation by substitude dis <- function(x0,x1,y0,y1){sqrt((x0-x1)^2 +(y0-y1)^2)} for distm() .

algo.p2poly <- function(pt, poly){
  if(!identical(poly[1,],poly[nrow(poly),])){poly<-rbind(poly,poly[1,])}
  library(geosphere)
  n <- nrow(poly) - 1
  pa <- distm(pt, poly[1:n, ])
  pb <- distm(pt, poly[2:(n+1), ])
  ab <- diag(distm(poly[1:n, ], poly[2:(n+1), ]))
  p <- (pa + pb + ab) / 2
  d <- 2 * sqrt(p * (p - pa) * (p - pb) * (p - ab)) / ab
  cosa <- (pa^2 + ab^2 - pb^2) / (2 * pa * ab)
  cosb <- (pb^2 + ab^2 - pa^2) / (2 * pb * ab)
  d[which(cosa <= 0)] <- pa[which(cosa <= 0)]
  d[which(cosb <= 0)] <- pb[which(cosb <= 0)]
  return(min(d))
}

Example:

poly <- matrix(c(114.33508, 114.33616,
                 114.33551, 114.33824,
                 114.34629, 114.35053,
                 114.35592, 114.35951, 
                 114.36275, 114.35340, 
                 114.35391, 114.34715,
                 114.34385, 114.34349,
                 114.33896, 114.33917,
                 30.48271, 30.47791,
                 30.47567, 30.47356, 
                 30.46876, 30.46851,
                 30.46882, 30.46770, 
                 30.47219, 30.47356,
                 30.47499, 30.47673,
                 30.47405, 30.47723, 
                 30.47872, 30.48320),
               byrow = F, nrow = 16)
pt1 <- c(114.33508, 30.48271)
pt2 <- c(114.6351, 30.98271)
algo.p2poly(pt1, poly)
algo.p2poly(pt2, poly)

Outcome:

> algo.p2poly(pt1, poly)
[1] 0
> algo.p2poly(pt2, poly)
[1] 62399.81